vapilot2004-
Sorry, I read the OP too quickly.
I know the TAPS III combustor for the GE9X will use CMC liner panels. This seems like a safe first step for use of the material in a commercial engine as the liners are not highly loaded, function mostly as a thermal barrier, and would not be sensitive to surface recession.
I also read that GE will be
evaluating CMC turbine nozzle guide vanes and HP turbine blades on their GE9X test rig. But I doubt these more demanding applications will make it onto the GE90 engine model for the 777X. The technology is still relatively new, and there still needs to be more work done with regards to durability/reliability, QC in production, in-service NDI, etc.
I also believe your comment about CMC materials eliminating the need for film cooling of turbine inlet nozzle guide vanes and HP turbine blades may not be entirely correct. As I understand it, internal air cooling and film cooling of these CMC components is still necessary, but the amount of bleed air flow is reduced. The reduced demand for cooling bleed air flow allows a greater percentage of the HP compressor flow to be directed through the combustor mixing nozzles.
Here is a picture of a TAPS combustor test rig with CMC liners. You can clearly see the air film cooling holes.
Here is a link to a NASA tech report describing some of the issues surrounding the use of CMCs for turbine engine hot section components.
The use of CMC materials does not really allow higher peak cycle temperatures in the engine. CMCs basically improve cycle efficiency by reducing thermal losses. Peak combustion cycle temperatures in commercial turbofan engines are currently limited by NOx formation, and NOx compounds only form when there is excess oxygen present at the flame front with temperatures greater than about 2800degF. The dilution air flow directed into the combustor helps to minimize NOx content of the exhaust gas, but I don't think it is an efficient way to regulate TIT.
Lastly, the biggest benefit of CMCs (as well as CFRP fan blades and Ti-Al HPC & LPT blades) on commercial turbofan engines is the significant weight savings they can potentially provide.